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IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Applications of time series models

The sample partial autocorrelation function of a stationary series of 400 observations shows significant spikes at lags 1 and 2 and is negligible beyond lag 2. The sample ACF decays gradually. Which model is the most appropriate tentative choice?

AR(2) is the appropriate tentative model because the partial autocorrelation function cuts off after lag 2 while the autocorrelation function tails off gradually. That is the signature of an autoregressive process of order two, whereas a moving average would show the opposite pattern.

  1. AMA(2)
  2. BAR(1)
  3. CARMA(1,1)
  4. DAR(2)Correct
  5. White noise

Explanation

An AR(p) process has a PACF that cuts off after lag p and an ACF that decays gradually. Here the PACF cuts off after lag 2, so AR(2) is indicated. An MA(2) would show the reverse pattern, with the ACF cutting off at lag 2.

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